A political campaign manager aims to assess the effectiveness of a new advertisement featuring Candidate X. The manager takes a random sample of 300 voters before the ad airs and another random sample of 250 voters afterward. In the "before" sample, 158 voters express support for Candidate X, while 140 voters in the "after" sample indicate their support. Let Pa​ represent the proportion of all voters supporting Candidate X after the ad is aired, and Pb​ represent the proportion before the ad is aired. Which of the following is the correct standardized test statistic for H0​:Pa​−Pb​=0?

(a) 0.56−0.527​/√(0.56×0.44)/​300+(0.527×0.473)/250​​
(b) ​​0.56−0.527​/√(0.542×0.458)/250​+(0.542×0.458)/300
(c) 0.56−0.527​/√(0.56×0.44)​/250+(0.527×0.473)​​/300
(d) 0.56−0.527​/√(0.542×0.458)​​/550
(e) 0.56−0.527​/√(0.56×0.527)​/250+(0.56×0.527)​​/300